From Parallelograms to Triangles

Student Summary

A parallelogram can always be decomposed into two identical triangles by a segment that connects opposite vertices.

Three parallelograms showing decompositions into two identical triangles.

Going the other way around, two identical copies of a triangle can always be arranged to form a parallelogram, regardless of the type of triangle being used. To produce a parallelogram, we can join a triangle and its copy along any of the three sides that match, so the same pair of triangles can make different parallelograms. Here are examples of how two copies of both Triangle A and Triangle F can be composed into three different parallelograms.

Three parallelograms composed from two identical triangles.

Three parallelograms composed from two identical triangles.

This special relationship between triangles and parallelograms can help us reason about the area of any triangle.

Visual / Anchor Chart

Standards

Addressing
6.G.1

Find area of triangles, trapezoids, and other polygons by composing into rectangles or decomposing into triangles and quadrilaterals. Apply these techniques in the context of solving real-world and mathematical problems.

Building Toward
6.G.1

Find area of triangles, trapezoids, and other polygons by composing into rectangles or decomposing into triangles and quadrilaterals. Apply these techniques in the context of solving real-world and mathematical problems.